Neutron spin-echo studies of bicontinuous microemulsions

2 Neutron spin-echo studies of bicontinuous microemulsions 

Only a small number of studies have addressed the problem of direct measurements of the dynamics of the surfactant layer in a bicontinuous microemulsion [16, 73, 75, 76]. The Zilman-Granek (ZG) model, which assumes membrane Zimm dynamics on an ensemble of free membrane patches [75] is expected to be applicable to the problem. In the framework of this model the intermediate scattering functions should then be describable by a stretched exponential function of the type 

The exponent is fixed to 2/3 similar to the Zimm polymer dynamics. Within the approximations used in [75] to arrive at a closed analytical expression, the slope and the elastic constant k are connected by 

i is the cosine of the angle between q and the surface normal, km-m is a cut-off describing the most extended bending mode, which still fits into the persistent surface area with size f, and J0 is the Bessel function of the order 0. This approach was already used to describe experimental intermediate scattering functions [76] and an example will be given in the next subsection. The same method also applies to lamellar phases since only persistent areas are assumed and no further assumptions about the geometry of the surfactant layer are made. 

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